1. Exercise 4E Write the following scales in the form of 1:n, where n is a whole number. (a) 5 cm represents 4 m (c) 5 cm represents 4 km (d) 4 cm represents 5 km​

Answer:

The correct graph of the given function is option C. Y.

Step-by-step explanation:

The correct graph is option B (X) because it satisfies all the conditions specified in the function definition.

The first segment of the graph starts at x=-2 and goes to the left, passing through the point (-4,-4) and representing the equation 2x+4. The second segment of the graph starts at x=-2 and goes to the right, passing through the point (2,3) and representing the equation 4+1/2x. The third segment of the graph starts at x=2 and goes to the right, passing through the point (5,0) and representing the equation -x+5.

Option A (W) has a line that passes through the point (2,6), which is not on the graph of the function, and option C (Y) has a line that passes through the point (2,5), which is also not on the graph of the function. Option D (Z) has an open circle at (-2,3), which should be a closed circle according to the function definition, and a closed circle at (2,5), which should be an open circle according to the function definition.

We can be 95% confident that the true mean playing time of all Willie Nelson recordings is between 48.89 and 53.71 minutes.

Using a t-multiplier for a 95% confidence interval with 39 degrees of freedom (n-1), we get t* = 2.022.

The margin of error is t* times the standard error of the mean, which is s / sqrt(n), where n is the sample size.

Thus, the margin of error is 2.022 * (5.8 / sqrt(40)) = 2.41 minutes.

To construct the confidence interval, we add and subtract the margin of error to the sample mean:

Lower limit = 51.3 - 2.41 = 48.89

Upper limit = 51.3 + 2.41 = 53.71

Therefore, we can be 95% confident that the true mean playing time of all Willie Nelson recordings is between 48.89 and 53.71 minutes.

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The relationship between the two variables negative linear association.

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association).

Linear relationships can be represented graphically or mathematically as the equation y = mx + b.

Given:

The data table is organized as follows:

1         2          3         4          5

32       26        20       14        8

We see that more the number of members in the team increase, the more the times decrease.

The correlation is a negative linear association, we conclude.

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The probability that a woman is actually pregnant given that the test is positive is 0.974 (or 97.4%).

a) To find the probability that a woman is actually pregnant given that the test is positive, we can use Bayes' theorem:

P(p|+) = P(+|p) P(p) / P (+)

where P(p) is the prior probability of a woman being pregnant (which is 0.82), P (+) is the probability of a positive test result, and P(+|p) is the conditional probability of a positive test result given that the woman is pregnant.

We are given that the test has a false positive rate of 0.02, which means that P(+|~p) = 0.02 (where ~p denotes "not pregnant"). We are also given that the test has a correct positive rate of 0.95, which means that P (+|p) = 0.95. Therefore, we can calculate:

P (+) = P(+|p) P(p) + P(+|~p) P(~p)

= 0.95 * 0.82 + 0.02 * (1 - 0.82)

= 0.802

Substituting into Bayes' theorem, we get:

P(p|+) = 0.95 * 0.82 / 0.802

= 0.974

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Answer:

Quadrant II

Step-by-step explanation:

sin (∅) > 0 means sin (∅)is positive

sec (∅) < 0 means sec (∅) is negative

thus,

∅ lies in quadrant II

In the linear equation, The value of the x and y are 11/6, -5 and  18/4.

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

here, we have,

We have to find that the value of the x and the y.

From the given information:

The equations are :

(4y - 18)

(6x - 11)

(x + 5)​

Now take all equation equal to zero.

Then

4y - 18 = 0

y = 18/4

And then

6x - 11 = 0

x = 11/6

And then

x + 5 = 0

x = -5.

So, In the linear equation, The value of the x and y are 11/6, -5 and  18/4.

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Part A: the system of inequalities has a definite solution to it.

Part B: Yes the point is a part of Solution Area

What is Linear Inequality?

In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

Solution:

The inequalities 4x + 2y ≤ 16

And x + y ≥ 4 is attached below please refer to it.

Part A: The graph of both inequalities intersects each other therefore the system of inequalities has a definite solution to it.

Part B: Yes point (2, 3) is included in the solution area, the following is the mathematical proof.

Using substitution 4*2 + 2*3 ≤ 16

8+6 ≤ 16

14 ≤ 16

And 2+3 ≥ 4

5 ≥ 4

Hence, the point is included in the solution area.

Part C:

Let’s assume a point 1,1 in the solution set so it implies that only the inequality 4x + 2y ≤ 16 is satisfied. Thus, not giving a feasible solution.

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Answer:

7)  216 ft²

8)  106 yd²

9)  200 m²

Step-by-step explanation:

To calculate the area of each given figure, subtract the area of the cut-out rectangle (marked in blue on the attached diagram) from the area of the larger rectangle.

[tex]\boxed{\begin{minipage}{5cm}\underline{Area of a rectangle}\\\\$A=w\cdot l$\\\\where:\\ \phantom{ww} $\bullet$ \quad $w$ is the width.\\ \phantom{ww} $\bullet$ \quad $l$ is the length.\\\end{minipage}}[/tex]

Note: The height of the larger rectangle is not complete. I have assumed it is 12 ft.

[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Larger rectangle}-\textsf{Cut-out rectangle}\\&=21 \cdot 12- 6\cdot 6\\&=252-36\\&=216\; \sf ft^2\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Larger rectangle}-\textsf{Cut-out rectangle}\\&= 17\cdot 10- (17-9)\cdot 8\\&= 17\cdot 10- 8\cdot 8\\&=170-64\\&=106\; \sf yd^2\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Total Area}&=\textsf{Larger rectangle}-\textsf{Cut-out rectangle}\\&= 15\cdot 20- 10\cdot 10 \\&=300-100\\&=200\; \sf m^2\end{aligned}[/tex]

The percentage decrease in the temperature is 87.13 %.

The percentage formula is dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

The temperature of a mixture changes from 121(1/4)°F to 15(3/5)°F.

This means,

Initial temperature = 121(1/4) = 485/4

Final temperature = 15(3/5) = 78/5

The change in temperature.

= 78/5 - 485/4

=  (312 - 2425)/20

= 2113/20

= - 105(13/20)

This means,

There is a decrease in temperature.

Now,

The percentage decreased.

= 105(13/20) / (485/4) x 100

= (2113/20) / (485/4) x 100

= 2113/20 x 4/485 x 100

= 2113/2425 x 100

= 87.13%

Thus,

The percentage decrease in the temperature is 87.13 %.

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The correlation coefficient of X and Y is 1, since their joint density is always positive for x ≤ y.

The correlation coefficient of two continuous random variables X and Y is a measure of how similar the two variables are in terms of their behavior. In this case, X and Y have a joint density of e−y, for 0 < x ≤ y < ∞ and 0 otherwise. This implies that the correlation coefficient of X and Y is 1, since their joint density is always positive for x ≤ y. This means that there is a perfect linear relationship between the two variables, meaning that as one variable increases, the other will also increase by the same amount.

To calculate the correlation coefficient, we need to calculate the covariance and variances of X and Y. The covariance is calculated by integrating the joint density of X and Y over the given range. The variance of X and Y is then calculated by taking the square root of the expected value of the squares of the differences between the expected value of X and Y and their respective observed values. Since the joint density of X and Y is always positive for x ≤ y, the correlation coefficient of X and Y will always be 1.

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Answer: A gallon of stain covers 70 square feet, so 8 gallons would cover 8 x 70 = 560 square feet. If Joaquin must apply 2 coats to the deck, he needs enough stain to cover the deck twice, so he needs 560 square feet x 2 = 1120 square feet.

Of the deck sizes listed, the largest one that Joaquin can fully cover with 2 coats of stain is 14 x 20 = 280 square feet, which is less than 1120 square feet. This means that Joaquin can fully cover all of the listed deck sizes if he must apply 2 coats of stain.

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

[tex]\sqrt{64}[/tex] -10 + 13

8 - 10 + 13

-2 + 13

11

P(success I at least 60 years old) = 0.125.

The possibility of an event in time is known as a probability in mathematics. How frequently does the incidence occur over the course of a specific time period, in plain English?

Given:

Over 1000 people try to climb mt Everest every year.

Of those who try to climb Everest, 31 percent succeed.

The probability that a climber is at least 60 years old is 0.04.

The probability that a climber is at least 60 years old and succeeds in climbing Everest is 0.005.

P(success I at least 60 years old) = 0.005/0.04 = 0.125

Therefore, the probability is 0.125.

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Hence, The value of y = 12 when x = -6.

Given that , Y varies directly with x .

If y=−4 when x=2,

Find y when x=−6.

According to the question,

This is a direct variation , y = kx

If,

y = −4  when x=2,

y = kx

-4 = 2k

k = -2

To find ;

y when x = −6

y = kx

y = (-2) (-6)

y = 12

The volume of the solid is [tex]4a^2h[/tex].

Each square cross-section has a side length equal to the diameter of the circle, which is 2a.

Therefore, the area of each cross-section is

[tex](2a)^2 = 4a^2[/tex]

The volume of the solid can be found by integrating the area of the cross sections over the height of the solid.

Since the cross-sections are perpendicular to the base, the height of each cross-section is equal to the thickness of the solid, which we can denote as dx.

Thus, the volume of the solid is given by the integral of the cross-sectional area with respect to x, from x = 0 to x = h, the height of the solid:

V = ∫ (0 to h) [tex]4a^2 dx[/tex]

V = [tex]4a^2[/tex] ∫(0 to h) dx

V = [tex]4a^2[/tex] (0 to h)

V = [tex]4a^2[/tex] (h - 0)

V = [tex]4a^2h[/tex]

Therefore, the volume of the solid is [tex]4a^2h[/tex]

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The solution is, the value of x = 5+ 8√2, 5- 8√2

Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

here, we have,

given that,

(x - 5)² +15=143

we know, (a-b)^2 = a^2 -2ab + b^2

so, we get,

x^2 - 10x + 25+15 = 143

or, x^2 -10x -103 = 0

now, solving we get,

x = 5+ 8√2, 5- 8√2

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The mean and the standard deviation for the data-set are given as follows:

mean = 23.8; standard deviation = 5.2.

The mean of a data-set is given by the sum of all the observations in the data-set divided by the number of observations, hence:

Mean = (8.2 + 13.4 + 18.6 + 23.8 + 29 + 34.92 + 39.4)/7

Mean = 23.8.

The standard deviation is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of observations, hence:

s = sqrt([(8.2-23.8)² + (13.4-23.8)² + (18.6-23.8)² + (23.8-23.8)² + (29-23.8)² + (34.92-23.8)² + (39.4-23.8)²]/7)

s = 5.2.

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The common volume of the two spheres is 5πr³/6. Since the two spheres are identical, the volume of the common portion is twice the volume of the spherical cap.

Since the distance between the centers of the two spheres is r/2, a cross-section of the two spheres and the plane perpendicular to their centers of symmetry will form an isosceles triangle with height h=r/2 and base 2√(r²-(r/2)²). The intersection of the two spheres will be a spherical cap with height h and radius r. The volume of this spherical cap is

V_cap = (1/3)π[tex]h^2[/tex](3r-h).

Since the two spheres are identical, the volume of the common portion is twice the volume of the spherical cap, so

Substituting h=r/2, we get

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The flight takes a total of  3 hours 45 minutes

From the question, we have the following parameters that can be used in our computation:

Inital time = 3:30 pm EST

Final time = 4:15 pm PST

When converted, we have

Inital time = 12:30 pm PST

Final time = 4:15 pm PST

So, we have

Difference = 4:15 pm PST -  12:30 pm PST

Evaluate the difference

Difference = 3 hours 45 minutes

Hence, the diration is 3 hours 45 minutes

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The general rule of the arithmetic sequence is given as follows:

[tex]a_n = -1 + 2(n - 1)[/tex]

The terms are given as follows:

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The nth term of an arithmetic sequence is given by the following rule:

[tex]a_n = a_1 + (n - 1)d[/tex]

The difference between the 3 terms is of 6, hence the common difference is given as follows:

3d = 6

d = 2.

As the 2nd term is of 1, the first term is of:

[tex]a_1 = 1 - 2 = -1[/tex]

Hence the rule is given as follows:

[tex]a_n = -1 + 2(n - 1)[/tex]

The terms are given as follows:

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Answer: Jason made $16

Step-by-step explanation:

Start by using the ratio of 2:3 to find the fraction of the total profit that Jason earned: Jason's share: 2/(2+3) = 2/5

Caleb's share: 3/(2+3) = 3/5

We can then use this fraction to calculate how much money Jason made:

Jason's share = (2/5) x $40 = $16

Therefore, Jason made $16 from the lemonade stand profits.

Answer: Let's assume that each of the 12 collectors donates n paintings. Then the total number of paintings donated will be 12 * n. We know that the total number of paintings donated by all collectors is 48, so we have the equation:

12 * n = 48

Dividing both sides by 12, we find that each collector donates n = 4 paintings. So, if Sergio has p paintings in his collection, after his donation he will have p - 4 paintings in his collection. The final answer is:

p - 4

Step-by-step explanation:

From the given data the probability that a respondent 18-29 years and 30+ years are 0.536 and 0.654 espectively. The probability that they answer yes (i.e. global warming will have an impact on them during their lifetime) is 0.265. There also appears to be a difference between ages 18-29 and 30+ regarding concern over global warming.

The probability that a respondent 18-29 years of age thinks that global warming will not pose a serious threat during his/her lifetime is:

P(18-29 and No) = 293/(134 + 293 + 117) = 0.536

The probability that a respondent 30+ years of age thinks that global warming will not pose a serious threat during his/her lifetime is:

P(30+ and No) = 432/(131 + 432 + 178) = 0.654

For a randomly selected respondent, the probability that they answer yes (i.e. global warming will have an impact on them during their lifetime) is:

P(Yes) = (134 + 131)/(134 + 131 + 293 + 432 + 117 + 178) = 0.265

Yes, there appears to be a difference between ages 18-29 and 30+ regarding concern over global warming. The probability of a respondent 30+ years of age thinking that global warming will not pose a serious threat during their lifetime (0.654) is higher than the corresponding probability for respondents 18-29 years of age (0.536). This suggests that older respondents are less concerned about global warming than younger respondents. However, a formal statistical test would be needed to confirm this difference.

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The expression that represents the number of inches the plant grew is 8 - x.

An expression is combination of variables, numbers and operators.

A plant measured x inches tall last week and 8 inches tall this week.

We have to find the expression which represent the plant grew this week.

The number of inches the plant grew can be represented by the difference between its height this week and its height last week.

Eight minus x is the required expression.

8 - x

Hence,  the expression that represents the number of inches the plant grew is 8 - x.

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Complete question

A plant measured x inches tall last week and 8 inches tall this week. Represent the number of inches the plant grew

A. X - 8

B. 8 - X

For the expression not chosen, describe a situation that the expression might represent.

Answer:

Step-by-step explanation:

If James gave each cousin 3 cupcakes, there would be 25 left. James is 71 cupcakes short of being able to give each cousin 15 cupcakes. You want to know the number of cousins and the number of cupcakes.

The given relations between the number of cupcakes (n) and the number of cousins (c) are ...

  n -3c = 25 . . . . . 3 each ⇒ 25 left

  n -15c = -71 . . . . . 15 each ⇒ 71 short

Subtracting the second equation from the first, we have ...

  (n -3c) -(n -15c) = (25) -(-71)

  12c = 96

  c = 8 . . . . . . divide by 12

  n = 3c +25 = 24 +25 = 49

(a) James has 8 cousins.

(b) James baked 49 cupcakes.

Answer:

second

Step-by-step explanation:

We cannot deduce anything about the p-value for age in the regression summary from just the 90% and 95%. cis for the parameter associated with age.

The 90% and 95% cis for the parameter associated with age tell us the range of values that the parameter could take, given the data. This range does not tell us anything about how likely the parameter is to take any of these values.

To determine how likely it is to take any of these values, we need to look at the p-value for age in the regression summary. The p-value tells us the probability that the parameter associated with age is different from zero.

It is the level of significance and is used to determine if the parameter is statistically significant. It is the only way to determine the likelihood of the parameter taking any of the values in its 90% and 95% cis.

Therefore, we cannot deduce anything about the p-value for age in the regression summary from just the 90% and 95% cis for the parameter associated with age.

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The additional factors that might have an effect on the stress levels of tea drinkers are called confounding variables. Confounding variables are variables that are not the main focus of the study but may have an impact on the results.

The term used to describe these additional factors that might have an effect on the stress levels of tea drinkers is "confounding variables." Confounding variables are extraneous factors that can affect the relationship between two variables of interest and can lead to incorrect conclusions about the relationship. In this case, the higher proportion of yoga practitioners and the increased exercise among tea drinkers could be considered confounding variables because they may be influencing the observed relationship between tea drinking and lower stress levels, rather than tea consumption alone.

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Out of the following the statement  has a reference angle of 30° and is in quadrant one or two-  is true of the location of the terminal side of an angle 0 whose sine value is 1/2.

Since the reason behind this is that the sine value of 1/2  can be written as sin(30°), this means that the terminal side of the angle is located at 30°, which is either quadrant one or two. Quadrant one is the upper right quadrant of the coordinate plane, and quadrant two is the upper left quadrant.

The reference angle of an angle is the angle between the terminal side of the angle and the positive x-axis. In this case, the reference angle would be  30°. The reference angle of an angle is important because it is used to determine the quadrant in which the terminal side of the angle is used to determine the quadrant in which the terminal side of the angle is located. The reference angle must be less than 90° in order for the terminal side to be located in the first and second quadrants.

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